President Barack Obama is sending a pointed message to Republicans by nominating Jack Lew as Treasury Secretary: I'm not backing down from this budget fight.

This is certainly a blow to any hope that Republicans might have had that Obama would flinch from his pledge not to negotiate over the debt ceiling. The president has said he will demand a clean bill raising the debt ceiling, unattached to any conditions or spending cuts.

When Senate GOP leader Mitch McConnell called Vice President Joe Biden as the deadline to cut a deal to avoid the fiscal cliff loomed, it was a sign of the tensions between the senator and Lew. McConnell had to create a new channel for negotiations because he could no longer go through the White House.

Here's how Manu Raju at Politico.com describes the tensions between Lew and Republicans:

Several Republicans said Tuesday they don't view Lew as a man interested in hearing GOP concerns. One aide called him "tone deaf" in understanding the compromises that Republicans could accept during high-stakes talks.

"No matter what you're proposing or no matter what compromise you're trying to forge, he comes at it from a position of, 'Whatever you want, I have to be against,'" the GOP aide said. "It doesn't advantage him in the negotiation, he doesn't get a different policy outcome than he would otherwise. It just irritates people. … It's as much personality as anything else."

These tensions are not new. Lew alienated Republican lawmakers during the summer of 2011 when he was director of the White House Office of Management and Budget. According to Brendan Miniter's book Leading from Behind, House Speaker John Boehner complained during the 2011 debt ceiling negotiations that he simply could not negotiate with Lew. (Read More:No More Mr. Nice Guy: New Battles Ahead for Obama)

"Whatever Boehner proposed, Lew would spurn in favor of his own, usually more complicated ideas. And Lew returned again and again to proposals Boehner had unambiguously refused. Lew had lost the trust of the House Republicans," Miniter writes.

Noam Scheiber's The Escape Artists tells the story of a meeting between Lew and Sen. Jon Kyl and fellow Republican Rep. Eric Cantor in the summer of 2011 to negotiate a deal to lift the debt ceiling. At one point Kyl and Cantor are clearly flustered at the stony resistance they are getting from Lew and Gene Sperling, the director of the National Economic Council.

"Let me get this right," Kyl says to Lew and Sperling. "You are saying there are Medicare savings you think would be good policy. But you won't do them unless we agree to raise taxes?"

The answer from Sperling and Lew was "yes." The negotiations quickly broke down.

There's no doubt that Lew is highly experienced and has shown a high level of loyalty to Obama. As a long time public servant, he knows the ins and outs of the budget better than most people. But even if Lew is respected in Washington, he's not a guy who is likely to be able to diminish the political acrimony.

If Obama wanted to appoint a man who could personify his no negotiation pledge, there would be no better pick than Lew.